A Jackknife Approach to Error-Reduction in Nonlinear Regression Estimation

The problems involving the use of jackknife methods in estimating the parameters of non linear regression models have been identified in this paper. We developed new algorithms for the estimation of nonlinear regression parameters. For estimating these parameters, computer programs were written in R for the implementation of these algorithms. We adopted the Gauss-Newton method based on Taylor’s series to approximate the nonlinear regression model with the linear term, and subsequently employ least square method iteratively. In the estimation of the nonlinear regression parameters, the results obtained from numerical problems using the Jackknife based algorithm developed yielded a reduced error sum of squares than the analytic result. As the number of d observations deleted in each resampling stage increases, the error sum of squares reduces minimally. This reveals the appropriateness of the new algorithms for the estimation of nonlinear regression parameters and in the reduction of the error terms in nonlinear regression estimation.